The maximum capacity and/or transmission distance in optical fibre communications links is no longer limited primarily by linear processes, such as chromatic dispersion and polarisation mode dispersion (PMD), or by additive noise. A variety of optical and electronic technologies are available, for use in incoherent and coherent communications links, which are able to fully compensate for linear dispersion effects. In addition, efficient and cost-effective optical amplification technologies, such as Erbium-Doped Fibre Amplifiers (EDFAs) are able to boost transmitted signal power in order to maintain an adequate Optical Signal-to-Noise Ratio (OSNR) for reliable recovery of the transmitted information.
As a result, the ultimate limit of transmission capacity and/or reach is generally nonlinear propagation effects, such as cross-phase modulation (XPM) in single-mode optical fibres. Amplifying the transmitted signals to ever-higher power levels results in excessive distortion due to optical nonlinearities. To avoid this, transmitted signal power must be limited, which reduces the available OSNR. In practice, the transmission of optical signals close to the limits of capacity and/or reach requires a trade-off between the nonlinear distortion and the accumulated optical noise in order to achieve an adequate quality in the received signal.
Further improvements in the transmission capacity or reach of optical links may be achieved by compensating for, or at least mitigating, the nonlinear distortions. Computational techniques are known that are able to substantially reverse (within limits determined by the presence of random noise processes) the nonlinear signal distortions. For example, for every real optical fibre transmission link there exists a corresponding theoretical ‘inverse link’, having characteristics that are precisely the reverse of the real link. While the ‘inverse link’ does not exist in reality, it may be simulated using computational techniques applied to an inverse link model. Propagation through the inverse link model may be computed either at the transmitting end, whereby a predistorted signal is transmitted and the predistortion reversed in the transmission link, or at the receiver, whereby a distorted signal is detected, and propagation through the inverse link model is simulated in order to recover the transmitted signal.
The inverse model technique is, however, highly computationally intensive. As a result, it is impractical to perform the necessary pre-compensation or post-compensation in real-time on a live optical transmission link. Solutions to this problem include pre-calculating suitable predistorted waveforms corresponding with various transmitted symbol sequences, or employing simplified computational techniques for mitigating nonlinear effects in real-time. All such approaches are, however, necessarily approximations to a full compensation calculation, and therefore achieve imperfect results.
Whether or not nonlinear mitigation technologies are employed, it is therefore desirable to use transmission formats that are relatively robust to nonlinear effects. In particular, it has been recognised that transmitting information over an optical link in the form of a number of lower bandwidth signals at different frequencies, e.g. via various Wavelength Division Multiplexing (WDM), optical frequency division multiplexing or Subcarrier Multiplexing (SCM) techniques, improves the nonlinear performance, because each of the narrower bandwidth channels is more robust in the presence of nonlinear effects than a corresponding single high bit-rate channel. For example, Optical Orthogonal Frequency Division Multiplexing (O-OFDM) transmits data on multiple lower-rate subcarriers in parallel, and employs a subcarrier spacing equal to the symbol rate of each subcarrier in order to achieve high spectral efficiency while avoiding linear cross-talk. Electrically-generated O-OFDM typically uses long symbols corresponding with hundreds of closely spaced subcarriers. This contrasts, at the other extreme, with conventional high bit-rate single-carrier systems, in which one high symbol-rate signal is transmitted on each optical wavelength carrier. Between these two extremes, systems have been developed such as No-Guard Interval (No-GI) coherent optical OFDM, coherent WDM, and Nyquist WDM, which employ optically-generated subcarriers that are orthogonal or near-orthogonal. Symbol lengths in such systems are shorter than electrically generated O-OFDM, but longer than single carrier systems.
It has been shown experimentally and theoretically that a large number of orthogonal carriers can be used to form a continuous optical spectrum capable of transmitting signals of in excess of 1 Tb/s.
Due to the very high potential capacity of such systems, it is desirable to provide further improvements to their performance in the presence of nonlinear propagation effects. It is, accordingly, an object of the present invention to provide such improvements.